Question

Giải các phương trình sau

 

1) \(x^2-\sqrt{x+5}=5\)

2) \(2\sqrt{2x+4}+4\sqrt{2-x}=\sqrt{9x^2+16}\)

Answer 1

a)\(x^2-\sqrt{x+5}=5\)

Đk:\(x\ge-5\)

\(\Leftrightarrow\left(x^2-5\right)^2=\sqrt{\left(x+5\right)^2}\)

\(\Leftrightarrow x^4-10x^2+25=x+5\)

\(\Leftrightarrow x^4-10x^2+25-x-5=0\)

\(\Leftrightarrow\left(x^2-x-5\right)\left(x^2+x-4\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x^2-x-5=0\left(1\right)\\x^2+x-4=0\left(2\right)\end{cases}}\)

\(\Delta_{\left(1\right)}=\left(-1\right)^2-\left(-4\left(1.5\right)\right)=21\)

\(\Leftrightarrow x=\frac{\sqrt{21}+1}{2}\left(tm\right)\)

\(\Delta_{\left(2\right)}=1^2-\left(-1\left(1.4\right)\right)=17\)

\(\Rightarrow x=-\frac{\sqrt{17}+1}{2}\)